Spherical harmonics: \(\mathbf {B}_{\rm sph}(\mathbf {e}_{st}) = \mathbf {Y}_L(\theta , \phi ) \mathbf {R}(\mathbf {p}_{st})^{\top }\)  where \(\mathbf {Y}_L\)  is the list of Laplace's spherical harmonics [1]} used to encode the angular information and \(\mathbf {R}(\mathbf {p}_{st})\)  encodes the distance. We use spherical harmonic functions up to degree \(L\) , which gives us \(L^2\)  orthogonal basis in total. The angles \(\theta \)  and \(\phi \)  can be directly computed from \(\mathbf {n}_{st}\in \mathbb {R}^3\)  in \(\mathbf {e}_{st}\) . \(\mathbf {R}\)  uses a linear combination of the above sine basis functions computed from \(\mathbf {p}_{st} \in \mathbb {R}^4\)  in \(\mathbf {e}_{st}\)  (thus, \(4J\)  basis functions in total) to encode distance information. Specifically, \(\mathbf {R}(\mathbf {p}_{st}) = \mathbf {W}_{\rm rad} \mathbf {B}_{\rm sin}(\mathbf {p}_{st}) + \mathbf {b}_{\rm rad} \in \mathbb {R}^S\) , where \(\mathbf {W}_{\rm rad}\)  and \(\mathbf {b}_{\rm rad}\)  are learnable parameters. \(\mathbf {B}_{\rm sph}\)  is flattened into a vector before being passed into \(\mathbf {F}_{b}\) . The dimensionality of \(\mathbf {B}_{\rm sph}\)  is \(B=SL^2\) , where we set \(S\)  to be the dimensionality of \(\mathbf {p}_{st}\) .
